Effects of ambient pressure,gas temperature and combustion reaction on droplet evaporation

The effects of ambient pressure, initial gas temperature and combustion reaction on the evaporation of a single fuel droplet and multiple fuel droplets are investigated by means of three-dimensional numerical simulation. The ambient pressure, initial gas temperature and droplets’ mass loading ratio, ML, are varied in the ranges of 0.1–2.0 MPa, 1000–2000 K and 0.027–0.36, respectively, under the condition with or without combustion reaction. The results show that both for the conditions with and without combustion reaction, droplet lifetime increases with increasing the ambient pressure at low initial gas temperature of 1000 K, but decreases at high initial gas temperatures of 1500 K and 2000 K, although the droplet lifetime becomes shorter due to combustion reaction. The increase of ML and the inhomogeneity of droplet distribution due to turbulence generally make the droplet lifetime longer, since the high droplets’ mass loading ratio at local locations causes the decrease of gas temperature and the increase of the evaporated fuel mass fraction towards the vapor surface mass fraction.     

Experimental and numerical investigation of droplet evaporation under diesel engine conditions

Evaporation of mono-disperse fuel droplets under high temperature and high pressure conditions is investigated. The time-dependent growth of the boundary layer of the droplets and the influence of neighboring droplets are examined analytically. A transient Nusselt number is calculated from numerical data and compared to the quasi-steady correlations available in literature. The analogy between heat and mass transfer is tested considering transient and quasi-steady calculations for the gas phase up to the critical point for a single droplet. The droplet evaporation in a droplet chain is examined numerically. Experimental investigations are performed to examine the influence of neighboring droplets on the drag coefficients. The results are compared with drag coefficient models for single droplets in a temperature range from T = 293–550 K and gas pressure p = 0.1–2 MPa. The experimental data provide basis for model validation in computational fluid dynamics.     

Low pressure evaporative cooling of micron-sized droplets of solutions and its novel applications

For free molecular regime the mathematical model of low pressure evaporative cooling of binary droplets in gas flow is developed. The model includes five ordinary differential equations and takes into account effects such as the release of the latent heat of condensation of both components and the release of the latent heat of dissolution. Simulations were made for weak aqueous solutions of ammonia. It was discovered that compositions of gas flow and the aqueous solution affect the rate of evaporative cooling of droplets. The ratio of mass flow of solution and gas flow is also an important parameter. The cooling rate of such binary droplets can reach the value of about 2 × 10⁵ K/s.As first applications we consider the air cooler based on evaporative cooling of droplets. For pressure of 20–80 Torr in aerosol reactor, it is shown that in the cooler with length of about 1 m temperature of air flow may drop to about 10–15 °C.The second application is the formation of nanoparticle in evaporating multicomponent droplet with two volatile components. Simulation was made for aqueous solution of ammonia which is widely used by experimentalists and engineers now. Effects of the number of precursors in droplet and supersaturation in droplet on the final size of nanoparticles were investigated.     

The auto-ignition of single n-heptane/iso-octane droplets

Numerical simulations including detailed chemical and physical models are performed to investigate the influence of different physical parameters on the auto-ignition of n-heptane/iso-octane droplets in air. Simulations are performed for isobaric conditions with an ambient pressure of 8 bar and a droplet radius of 200 μm. The ambient gas temperature ranges from 800 K to 2000 K and the droplet temperature was varied from 300 K to 400 K. Below an ambient temperature of 1000 K the ignition delay time is found to increase with an increasing volume fraction of iso-octane. Above 1000 K the ignition delay time appears to be almost independent of the mixture composition of the droplet. The local ignition conditions are also studied. It turns out that ignition occurs at points, where the mixture is lean. This trend is more significant, if the ambient temperature increases. The influence of physical properties of the mixture components, like diffusion coefficients, heat conductivity, heat of vaporization and vapor pressure, is investigated. Furthermore, the influences of simplifying assumptions such as the distillation and diffusion limit are studied.     

Mist film cooling simulation at gas turbine operating conditions

Air film cooling has been successfully used to cool gas turbine hot sections for the last half century. A promising technology is proposed to enhance air film cooling with water mist injection. Numerical simulations have shown that injecting a small amount of water droplets into the cooling air improves film-cooling performance significantly. However, previous studies were conducted at conditions of low Reynolds number, temperature, and pressure to allow comparisons with experimental data. As a continuous effort to develop a realistic mist film cooling scheme, this paper focuses on simulating mist film cooling under typical gas turbine operating conditions of high temperature and pressure. The mainstream flow is at 15 atm with a temperature of 1561 K. Both 2D and 3D cases are considered with different hole geometries on a flat surface, including a 2D slot, a simple round hole, a compound-angle hole, and fan-shaped holes. The results show that 10–20% mist (based on the coolant mass flow rate) achieves 5–10% cooling enhancement and provides an additional 30–68 K adiabatic wall temperature reduction. Uniform droplets of 5–20 μm are used. The droplet trajectories indicate the droplets tend to move away from the wall, which results in a lower cooling enhancement than under low pressure and temperature conditions. The commercial software Fluent is adopted in this study, and the standard k–ε model with enhanced wall treatment is adopted as the turbulence model.     

Monodisperse droplet heating and evaporation: Experimental study and modelling

Results of experimental studies and the modelling of heating and evaporation of monodisperse ethanol and acetone droplets in two regimes are presented. Firstly, pure heating and evaporation of droplets in a flow of air of prescribed temperature are considered. Secondly, droplet heating and evaporation in a flame produced by previously injected combusting droplets are studied. The phase Doppler anemometry technique is used for droplet velocity and size measurements. Two-colour laser induced fluorescence thermometry is used to estimate droplet temperatures. The experiments have been performed for various distances between droplets and various initial droplet radii and velocities. The experimental data have been compared with the results of modelling, based on given gas temperatures, measured by coherent anti-stokes Raman spectroscopy, and Nusselt and Sherwood numbers calculated using measured values of droplet relative velocities. When estimating the latter numbers the finite distance between droplets was taken into account. The model is based on the assumption that droplets are spherically symmetrical, but takes into account the radial distribution of temperature inside droplets. It is pointed out that for relatively small droplets (initial radii about 65 μm) the experimentally measured droplet temperatures are close to the predicted average droplet temperatures, while for larger droplets (initial radii about 120 μm) the experimentally measured droplet temperatures are close to the temperatures predicted at the centre of the droplets.     

Modeling of thermo-physical processes in liquid ceramic precursor droplets injected into a plasma jet

Modeling of liquid ceramic precursor droplets axially injected into a plasma is presented. Droplets undergo heating and solvent vaporization leading to high solute concentration near droplet surface. At a critical solute super-saturation concentration, precipitation is postulated to occur forming a precipitate shell around liquid core. Internal pressurization and rupture of shell occur subsequently. Droplet size, shell porosity and thickness effects were studied. Timescales of internal pressurization and precipitate formation are of the order of microsecond and millisecond, respectively. Small droplets (d ⩽ 5 μm) tend to form thick shells and are less likely to undergo shell fracture compared to larger droplets.     

Effects of particle volume fraction on spray heat transfer performance of Al2O3–water nanofluid

An experimental investigation is conducted into the effects of the particle volume fraction on the spray heat transfer performance of a nanofluid comprising de-ionized water and Al₂O₃ particles with a diameter of 35 nm. The tests are performed with a flat, horizontal heated surface using a nozzle with an orifice diameter of 0.7 mm and a nozzle-to-heated surface distance of 17 mm. The spray mass flux is varied in the range of 26.433–176.751 kg/m² s, while the particle volume fraction is specified as 0%, 0.001%, 0.025%, or 0.05%. It is found that the optimal heat transfer performance is obtained using a particle volume fraction of 0.001%. The surface compositions of the sprayed samples are observed using scanning electron microscopy. The results show that the surfaces sprayed with a nanofluid containing 0.025 Vol% or 0.05 Vol% of nanoparticles contain a small amount of Al. However, those cooled using a nanofluid with a particle volume fraction of 0% or 0.001% show no traces of Al.     

New solutions to the species diffusion equation inside droplets in the presence of the moving boundary

Two new solutions to the equation, describing the diffusion of species during multi-component droplet evaporation, are suggested. The first solution is the explicit analytical solution to this equation, while the second one reduces the solution of the differential transient species equation to the solution of the Volterra integral equation of the second kind. Both solutions take into account the effect of the reduction of the droplet radius due to evaporation, assuming that this radius is a linear function of time. The analytical solution has been incorporated into a zero dimensional CFD code and applied to the analysis of a bi-component droplet evaporation. The case of an initial 50% ethanol–50% acetone mixture and droplets with initial diameter equal to 142.7 μm moving in air at atmospheric pressure has been considered. To separate the effect of the moving boundary on the species diffusion equation from a similar effect on the heat conduction equation inside droplets, described earlier, a rather artificial assumption that the droplet temperature is homogeneous and fixed has been made. It has been pointed out that the effect of the moving boundary slows down the increase in the mass fraction of ethanol (the less volatile substance in the mixture) and leads to the acceleration of droplet evaporation.     

Interaction of Marangoni convection with mass transfer effects at droplets

For the system water–acetone–toluene the mass transfer is measured up to a pressure of 200 bar at a constant temperature of 20 °C for two different concentrations at quiescent pendant droplets. The measurements are compared to empirical predictions. The influence of a surfactant is investigated.A three-mode magnetic suspension balance is used to measure the transfer. Additionally, a Schlieren optic is applied to visualise the convection.Only in case of the transfer direction from the droplet into the continuous phase Marangoni convection is detected. A good agreement of measurement and evaluation is achieved. The surfactant damps the interfacial convection.     

Tethered methanol droplet combustion in carbon-dioxide enriched environment under microgravity conditions

Tethered methanol droplet combustion in carbon dioxide enriched environment is simulated using a transient one-dimensional spherosymmetric droplet combustion model that includes the effects of tethering. A priori numerical predictions are compared against recent experimental data. The numerical predictions compare favorably with the experimental results and show significant effects of tethering on the experimental observations. The presence of a relatively large quartz fiber tether increases the burning rate significantly and hence decreases the extinction diameter. The simulations further show that the extinction diameter depends on both the initial droplet diameter and the ambient concentration of carbon dioxide. Increasing the droplet diameter and ambient carbon dioxide concentration both of them lead to a decrease in the burning rate and increase in the extinction diameter. The influence of ambient carbon dioxide concentration on extinction shows a sharp transition in extinction for larger size droplets (d_o > 1.5 mm) due to a change in the mode of extinction from diffusive to radiative control. In addition predictions from the numerical model is compared against a recently developed simplified theoretical model for predicting extinction diameter for methanol droplets, where the presence and heat transfer contribution of the tether is not taken into account implicitly. The numerical results suggest some limitation in the theoretical modeling assumptions for favorable comparisons with the experimental data.     

A numerical study on growth mechanism of dropwise condensation

Based on the intrinsic growth rate (R ～ T^1/3) of single droplet, processes of nucleation, growth, renucleation and sweeping of droplet are simulated in this paper. The influences of number of initial droplets on average radius, surface coverage and number of droplets on substrate are investigated. The simulation results show that the apparent growth rate of droplets is strongly dependent on the number of initial droplets. In addition, statistical fractal characteristic of droplet size distribution is found to be consistent with experimental measurements, and the drop size distribution is also found to be consistent qualitatively with that from experimental observations. The validity of the present simulations is thus verified. The present work may provide a great help in well understanding of the growth mechanism of dropwise condensation.     

Experimental study on spreading and evaporation of inkjet printed pico-liter droplet on a heated substrate

In this work, the spreading and evaporation of 2–70 pL droplet (17–50 μm diameter) of water and ethylene glycol jetted by drop-on-demand piezo-driven jetting head on the heated substrate are studied. According to the experimental results, the interfacial oscillation phenomena of water droplet whose Ohnesorge number (Oh) is about 10^?2 is similar to that in inviscid impact driven region, while that of ethylene glycol droplet (Oh ≈10^?1) is similar to that in highly viscous impact driven region followed by capillary driven extra spreading. In addition, various time scales used for nano/micro-liter droplets agree well with the times for interfacial oscillation, viscous damping, extra wetting, and evaporation in pico-liter droplets. In the case of water droplet, the spreading processes end before the evaporation becomes significant. However, in the case of highly viscous ethylene glycol droplet, the extra wetting overlaps the evaporation at high temperature.     

Soot formation from a distillation cut of a Fischer–Tropsch diesel fuel: A shock tube study

The kinetics of soot formation from Fischer–Tropsch (FT) fuels was studied in a heated shock tube under homogeneous conditions. Soot induction delay time and soot yield were measured between 10 and 17 atm using a distillation cut at 403 K of a Fischer–Tropsch fuel diesel. Two fuel concentrations were investigated in pyrolysis: 0.2% and 0.4% FT in Ar. Equivalence ratios (Φ) = 18 and 5 were also investigated for the highest fuel concentration. During this study, a second growth of the soot volume fraction profile was observed with the highest fuel concentration in pyrolysis and at Φ = 18. It was shown that this second growth appears only at temperatures higher than the temperature at which the soot yield is maximum. Under the conditions investigated, the soot induction delay time was found not to be very sensitive to the fuel concentration. A careful analysis of the soot volume fraction profiles showed that this finding was linked to the measurement method usually adopted. Nevertheless, this method was found adequate for a systematic comparison between different fuels or for an investigation of the oxygen concentration effects. The addition of oxygen to the mixture promotes soot formation in its early stages by decreasing the soot induction delay time. A shift of the soot yield curve toward lower temperatures was also observed. Moreover, oxygen addition reduces the amount of soot produced. This reduction is proportional to the O₂ concentration. Comparisons with literature data showed that a Fischer–Tropsch fuel primarily composed of n-paraffins can be correctly represented by an n-paraffin with a molecular size comparable to the average molecular size of the Fischer–Tropsch fuel. The maximum soot yield of the Fischer–Tropsch distillation cut studied was not significantly different from that of a diesel fuel surrogate previously studied (Mathieu et al., Combust. Flame 156 (2009) 1576–1586).     

The effect of confinement on the flow and turbulent heat transfer in a mist impinging jet

Numerical study of the effect of confinement on a flow structure and heat transfer in an impinging mist jets with low mass fraction of droplets (M_L1 ? 1%) were presented. The turbulent mist jet is issued from a pipe and strikes into the center of the flat heated plate. Mathematical model is based on the steady-state RANS equations for the two-phase flow in Euler/Euler approach. Predictions were performed for the distances between the nozzle and the target plate x/(2R) = 0.5–10 and the initial droplets size (d₁ = 5–100 μm) at the varied Reynolds number based on the nozzle diameter, Re = (1.3–8) × 10⁴. Addition of droplets causes significant increase of heat transfer intensity in the vicinity of the jet stagnation point compared with the one-phase air impinging jet. The presence of the confinement upper surface decreases the wall friction and heat transfer rate, but the change of friction and heat transfer coefficients in the stagnation point is insignificant. The effect of confinement on the heat transfer is observed only in very small nozzle-to-plate distances (H/(2R) < 0.5) both in single-phase and mist impinging jets.     

A quasi-discrete model for heating and evaporation of complex multicomponent hydrocarbon fuel droplets

A quasi-discrete model for heating and evaporation of complex multicomponent hydrocarbon fuel droplets is suggested and tested in Diesel engine-like conditions. The model is based on the assumption that properties of components are weak functions of the number of carbon atoms in the components (n). The components with relatively close n are replaced by the quasi-components with properties calculated as average properties of the a priori defined groups of actual components. Thus the analysis of heating and evaporation of droplets consisting of many components is replaced by the analysis of heating and evaporation of droplets consisting of relatively few quasi-components. In contrast to previously suggested approaches to modelling the heating and evaporation of droplets consisting of many components, the effects of temperature gradient and quasi-component diffusion inside droplets are taken into account. The model is applied to Diesel fuel droplets, approximated as a mixture of 21 components C_nH_2n+2 for 5 ? n ? 25, which correspond to a maximum of 20 quasi-components with average properties for n = n_j and n = n_j+1, where j varies from 5 to 24. It is pointed out that droplet surface temperatures and radii, predicted by a rigorous model taking into account the effect of all 20 quasi-components, are very close to those predicted by the model, using just five quasi-components. Errors due to the assumptions that the droplet thermal conductivity and species diffusivities are infinitely large cannot be ignored in the general case.     

Dispersion and vaporization of biofuels and conventional fuels in a crossflow pre-mixer

In lean premixed pre-vaporized (LPP) combustion, controlled atomization, dispersion and vaporization of different types of liquid fuel in the premixer are the key factors required to stabilize the combustion process and improve the efficiency. The dispersion and vaporization process for biofuels and conventional fuels sprayed into a crossflow pre-mixer have been simulated and analyzed with respect to vaporization rate, degree of mixedness and homogeneity. Two major biofuels under investigation are Ethanol and Rapeseed Methyl Esters (RME), while conventional fuels are gasoline and jet-A. First, the numerical code is validated by comparing with the experimental data of single n-heptane and decane droplet evaporating under both moderate and high temperature convective air flow. Next, the spray simulations were conducted with monodispersed droplets with an initial diameter of 80 μm injected into a turbulent crossflow of air with a typical velocity of 10 m/s and temperature of around 800 K. Vaporization time scales of different fuels are found to be very different. The droplet diameter reduction and surface temperature rise were found to be strongly dependent on the fuel properties. Gasoline droplet exhibited a much faster vaporization due a combination of higher vapor pressure and smaller latent heat of vaporization compared to other fuels. Mono-dispersed spray was adopted with the expectation of achieving more homogeneous fuel droplet size than poly-dispersed spray. However, the diameter histogram in the zone near the pre-mixer exit shows a large range of droplet diameter distributions for all the fuels. In order to improve the vaporization performance, fuels were pre-heated before injection. Results show that the Sauter mean diameter of ethanol improved from 52.8% of the initial injection size to 48.2%, while jet-A improved from 48.4% to 18.6% and RME improved from 63.5% to 31.3%. The diameter histogram showed improved vaporization performance of jet-A.     

Towards a predictive evaporation model for multi-component hydrocarbon droplets at all pressure conditions

In this paper, a new evaporation model for multi-component hydrocarbon droplets is proposed. Compared to previously published models, it has two new features. First, an expression of the Stefan velocity is proposed which ensures gas mass conservation. In addition, the evaporation rate of each species is obtained by the integration of the exact equation of species mass fraction. Second, the heat flux due to species diffusion is taken into account in addition to the classical conduction heat flux between the gas and the liquid droplets. The comprehensive multi-component droplets vaporization model including the above two features is presented for high and low pressure conditions, for which a real and a perfect fluid equation of state (EOS) has been used, respectively. Free convection is also taken into account using the Grashof number in the Kulmala–Vesala correlations [1] for the Sherwood and Nusselt numbers. The model is compared with very accurate experimental data which were recently obtained by Chauveau et al. (2008) [2] at atmospheric pressure and temperature ranges of 473–973 K for n-heptane and 548–623 K for n-decane droplets of 400 μm initial size. A very good agreement with the experimental data including micro-gravity conditions has been obtained. Indeed, the results have confirmed that the free convection process plays a significant role in the evaporation rate of liquid droplets under earth gravity and quiescent conditions. This shows the relevance of the new features of the model. The numerical results have also shown that real fluid EOS is not necessary at atmospheric pressure for the temperature range given above. In addition, the numerical results of the new model are also compared with the experimental data of Birouk (1996) [3] for two-component droplets of n-heptane and n-decane with different compositions of the liquid mixture. Finally, the non-ideality of the mixture is shown to become significant at high ambient pressures and especially at low ambient temperature conditions where a real-gas EOS is needed.     

Interfacial temperature measurements,high-speed visualization and finite-element simulations of droplet impact and evaporation on a solid surface

The objective of this work is to investigate the coupling of fluid dynamics, heat transfer and mass transfer during the impact and evaporation of droplets on a heated solid substrate. A laser-based thermoreflectance method is used to measure the temperature at the solid–liquid interface, with a time and space resolution of 100 μs and 20 μm, respectively. Isopropanol droplets with micro- and nanoliter volumes are considered. A finite-element model is used to simulate the transient fluid dynamics and heat transfer during the droplet deposition process, considering the dynamics of wetting as well as Laplace and Marangoni stresses on the liquid–gas boundary. For cases involving evaporation, the diffusion of vapor in the atmosphere is solved numerically, providing an exact boundary condition for the evaporative flux at the droplet–air interface. High-speed visualizations are performed to provide matching parameters for the wetting model used in the simulations. Numerical and experimental results are compared for the transient heat transfer and the fluid dynamics involved during the droplet deposition. Our results describe and explain temperature oscillations at the drop–substrate interface during the early stages of impact. For the first time, a full simulation of the impact and subsequent evaporation of a drop on a heated surface is performed, and excellent agreement is found with the experimental results. Our results also shed light on the influence of wetting on the heat transfer during evaporation.     

Modelling and experiments on vaporization of saline water at low temperatures and reduced pressures

A vapor diffusion model, which takes into account the reduction of droplet temperature during the evaporation process, was used to determine the achievable targets for desalination of seawater at temperatures between 26 °C and 32 °C when the saline water was injected as fine droplets in a low-pressure vaporizer. The temperatures between 26 °C and 32 °C correspond to the warm temperatures of the ocean surface in the tropics. The predictions from the model were verified by a large number of experiments at vacuum pressures between 10 mm and 18 mm mercury. The upper bound of the rate of flow of the saline water in the experiments was 1000 l/h. Typical evaporation time of the droplets was a few hundred milliseconds and this was less than the residence time of the spray provided for in the vaporizer. The yield of fresh water measured in the experiments was between 3% and 4% and matched well with the predictions. Small values of water injection pressures of about 0.1 MPa were found to be adequate when a swirl nozzle, used for garden sprays, was employed. Changes in the height of water injection in the vaporizer did not significantly influence the yield of fresh water.